Simplify the following expression and state the condition under which the simplification is valid: $p = \dfrac{a^2 - 2a}{a^2 - 12a + 20}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{a^2 - 2a}{a^2 - 12a + 20} = \dfrac{(a)(a - 2)}{(a - 10)(a - 2)} $ Notice that the term $(a - 2)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(a - 2)$ gives: $p = \dfrac{a}{a - 10}$ Since we divided by $(a - 2)$, $a \neq 2$. $p = \dfrac{a}{a - 10}; \space a \neq 2$